Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 94.5% → 97.9%

Time: 14.2s

Alternatives: 21

Speedup: 0.5×

• 37.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right) - \left(a \cdot \left(t + -1\right) + \left(z \cdot \left(y + -1\right) - x\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \left(y - b \cdot \frac{\left(\frac{a}{b} + \frac{x}{b}\right) + \left(y + -2\right)}{z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (-
          (* b (- (+ y t) 2.0))
          (+ (* a (+ t -1.0)) (- (* z (+ y -1.0)) x)))))
   (if (<= t_1 INFINITY)
     t_1
     (* z (- 1.0 (- y (* b (/ (+ (+ (/ a b) (/ x b)) (+ y -2.0)) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (1.0 - (y - (b * ((((a / b) + (x / b)) + (y + -2.0)) / z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (1.0 - (y - (b * ((((a / b) + (x / b)) + (y + -2.0)) / z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (1.0 - (y - (b * ((((a / b) + (x / b)) + (y + -2.0)) / z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(Float64(a * Float64(t + -1.0)) + Float64(Float64(z * Float64(y + -1.0)) - x)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(1.0 - Float64(y - Float64(b * Float64(Float64(Float64(Float64(a / b) + Float64(x / b)) + Float64(y + -2.0)) / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (1.0 - (y - (b * ((((a / b) + (x / b)) + (y + -2.0)) / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(1.0 - N[(y - N[(b * N[(N[(N[(N[(a / b), $MachinePrecision] + N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 36.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 29.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 29.3%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 29.3%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 29.3%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 29.3%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 29.3%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 29.3%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 56.6%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 56.6%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 56.6%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 29.3%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 56.6%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 56.6%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in z around -inf 55.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(y + -1 \cdot \frac{b \cdot \left(\left(y + \left(\frac{a}{b} + \frac{x}{b}\right)\right) - 2\right)}{z}\right) - 1\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 55.9%

         \[\leadsto \color{blue}{-z \cdot \left(\left(y + -1 \cdot \frac{b \cdot \left(\left(y + \left(\frac{a}{b} + \frac{x}{b}\right)\right) - 2\right)}{z}\right) - 1\right)} \]

      2. *-commutative 55.9%

         \[\leadsto -\color{blue}{\left(\left(y + -1 \cdot \frac{b \cdot \left(\left(y + \left(\frac{a}{b} + \frac{x}{b}\right)\right) - 2\right)}{z}\right) - 1\right) \cdot z} \]

      3. distribute-rgt-neg-in 55.9%

         \[\leadsto \color{blue}{\left(\left(y + -1 \cdot \frac{b \cdot \left(\left(y + \left(\frac{a}{b} + \frac{x}{b}\right)\right) - 2\right)}{z}\right) - 1\right) \cdot \left(-z\right)} \]

   9. Simplified 74.0%

      \[\leadsto \color{blue}{\left(\left(y - b \cdot \frac{\left(\frac{a}{b} + \frac{x}{b}\right) + \left(y + -2\right)}{z}\right) + -1\right) \cdot \left(-z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(y + t\right) - 2\right) - \left(a \cdot \left(t + -1\right) + \left(z \cdot \left(y + -1\right) - x\right)\right) \leq \infty:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - \left(a \cdot \left(t + -1\right) + \left(z \cdot \left(y + -1\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \left(y - b \cdot \frac{\left(\frac{a}{b} + \frac{x}{b}\right) + \left(y + -2\right)}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(y + Float64(t + -2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 95.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   2. fma-define 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   3. associate--l+ 97.2%

      \[\leadsto \mathsf{fma}\left(\color{blue}{y + \left(t - 2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   4. sub-neg 97.2%

      \[\leadsto \mathsf{fma}\left(y + \color{blue}{\left(t + \left(-2\right)\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   5. metadata-eval 97.2%

      \[\leadsto \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   6. sub-neg 97.2%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]

   7. associate-+l- 97.2%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x - \left(\left(y - 1\right) \cdot z - \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   8. fma-neg 97.6%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -\left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   9. sub-neg 97.6%

      \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(\color{blue}{y + \left(-1\right)}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   10. metadata-eval 97.6%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + \color{blue}{-1}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   11. remove-double-neg 97.6%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right) \cdot a}\right)\right) \]

   12. sub-neg 97.6%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot a\right)\right) \]

   13. metadata-eval 97.6%

       \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + \color{blue}{-1}\right) \cdot a\right)\right) \]

3. Simplified 97.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)} \]
4. Add Preprocessing

5. Final simplification 97.6%

   \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \]
6. Add Preprocessing

Alternative 3: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right) - \left(a \cdot \left(t + -1\right) + \left(z \cdot \left(y + -1\right) - x\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (-
          (* b (- (+ y t) 2.0))
          (+ (* a (+ t -1.0)) (- (* z (+ y -1.0)) x)))))
   (if (<= t_1 INFINITY) t_1 (* y (- b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(Float64(a * Float64(t + -1.0)) + Float64(Float64(z * Float64(y + -1.0)) - x)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((y + t) - 2.0)) - ((a * (t + -1.0)) + ((z * (y + -1.0)) - x));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.5%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(y + t\right) - 2\right) - \left(a \cdot \left(t + -1\right) + \left(z \cdot \left(y + -1\right) - x\right)\right) \leq \infty:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - \left(a \cdot \left(t + -1\right) + \left(z \cdot \left(y + -1\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-158}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -1.5e+145)
     (* b (- y 2.0))
     (if (<= b -5.6e-59)
       t_1
       (if (<= b -1.95e-158)
         x
         (if (<= b 1.7e-291)
           t_1
           (if (<= b 3e-189) x (if (<= b 1.7e+118) t_1 (* t b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.5e+145) {
		tmp = b * (y - 2.0);
	} else if (b <= -5.6e-59) {
		tmp = t_1;
	} else if (b <= -1.95e-158) {
		tmp = x;
	} else if (b <= 1.7e-291) {
		tmp = t_1;
	} else if (b <= 3e-189) {
		tmp = x;
	} else if (b <= 1.7e+118) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-1.5d+145)) then
        tmp = b * (y - 2.0d0)
    else if (b <= (-5.6d-59)) then
        tmp = t_1
    else if (b <= (-1.95d-158)) then
        tmp = x
    else if (b <= 1.7d-291) then
        tmp = t_1
    else if (b <= 3d-189) then
        tmp = x
    else if (b <= 1.7d+118) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -1.5e+145) {
		tmp = b * (y - 2.0);
	} else if (b <= -5.6e-59) {
		tmp = t_1;
	} else if (b <= -1.95e-158) {
		tmp = x;
	} else if (b <= 1.7e-291) {
		tmp = t_1;
	} else if (b <= 3e-189) {
		tmp = x;
	} else if (b <= 1.7e+118) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -1.5e+145:
		tmp = b * (y - 2.0)
	elif b <= -5.6e-59:
		tmp = t_1
	elif b <= -1.95e-158:
		tmp = x
	elif b <= 1.7e-291:
		tmp = t_1
	elif b <= 3e-189:
		tmp = x
	elif b <= 1.7e+118:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.5e+145)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= -5.6e-59)
		tmp = t_1;
	elseif (b <= -1.95e-158)
		tmp = x;
	elseif (b <= 1.7e-291)
		tmp = t_1;
	elseif (b <= 3e-189)
		tmp = x;
	elseif (b <= 1.7e+118)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -1.5e+145)
		tmp = b * (y - 2.0);
	elseif (b <= -5.6e-59)
		tmp = t_1;
	elseif (b <= -1.95e-158)
		tmp = x;
	elseif (b <= 1.7e-291)
		tmp = t_1;
	elseif (b <= 3e-189)
		tmp = x;
	elseif (b <= 1.7e+118)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e+145], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.6e-59], t$95$1, If[LessEqual[b, -1.95e-158], x, If[LessEqual[b, 1.7e-291], t$95$1, If[LessEqual[b, 3e-189], x, If[LessEqual[b, 1.7e+118], t$95$1, N[(t * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.5000000000000001e145

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 92.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 80.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 80.4%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 80.4%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 80.4%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 80.4%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 80.4%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 80.4%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 82.9%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 82.9%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 82.9%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 80.4%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 82.9%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 82.9%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in b around inf 57.2%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]

   if -1.5000000000000001e145 < b < -5.59999999999999961e-59 or -1.9499999999999998e-158 < b < 1.70000000000000013e-291 or 3e-189 < b < 1.69999999999999993e118

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -5.59999999999999961e-59 < b < -1.9499999999999998e-158 or 1.70000000000000013e-291 < b < 3e-189

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.6%

      \[\leadsto \color{blue}{x} \]

   if 1.69999999999999993e118 < b

   1. Initial program 88.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 94.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(1 - \frac{a}{b}\right)\right)} \]

   5. Taylor expanded in a around 0 52.8%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-158}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-211}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-141}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -6e+55)
     t_1
     (if (<= t -7e-154)
       (* y (- b z))
       (if (<= t 3.8e-211)
         x
         (if (<= t 1.85e-141)
           (* z (- 1.0 y))
           (if (<= t 4000000000.0) x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6e+55) {
		tmp = t_1;
	} else if (t <= -7e-154) {
		tmp = y * (b - z);
	} else if (t <= 3.8e-211) {
		tmp = x;
	} else if (t <= 1.85e-141) {
		tmp = z * (1.0 - y);
	} else if (t <= 4000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-6d+55)) then
        tmp = t_1
    else if (t <= (-7d-154)) then
        tmp = y * (b - z)
    else if (t <= 3.8d-211) then
        tmp = x
    else if (t <= 1.85d-141) then
        tmp = z * (1.0d0 - y)
    else if (t <= 4000000000.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6e+55) {
		tmp = t_1;
	} else if (t <= -7e-154) {
		tmp = y * (b - z);
	} else if (t <= 3.8e-211) {
		tmp = x;
	} else if (t <= 1.85e-141) {
		tmp = z * (1.0 - y);
	} else if (t <= 4000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -6e+55:
		tmp = t_1
	elif t <= -7e-154:
		tmp = y * (b - z)
	elif t <= 3.8e-211:
		tmp = x
	elif t <= 1.85e-141:
		tmp = z * (1.0 - y)
	elif t <= 4000000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6e+55)
		tmp = t_1;
	elseif (t <= -7e-154)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 3.8e-211)
		tmp = x;
	elseif (t <= 1.85e-141)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 4000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -6e+55)
		tmp = t_1;
	elseif (t <= -7e-154)
		tmp = y * (b - z);
	elseif (t <= 3.8e-211)
		tmp = x;
	elseif (t <= 1.85e-141)
		tmp = z * (1.0 - y);
	elseif (t <= 4000000000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+55], t$95$1, If[LessEqual[t, -7e-154], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-211], x, If[LessEqual[t, 1.85e-141], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4000000000.0], x, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.00000000000000033e55 or 4e9 < t

   1. Initial program 93.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 70.8%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -6.00000000000000033e55 < t < -7.0000000000000001e-154

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -7.0000000000000001e-154 < t < 3.80000000000000012e-211 or 1.85e-141 < t < 4e9

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 39.5%

      \[\leadsto \color{blue}{x} \]

   if 3.80000000000000012e-211 < t < 1.85e-141

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 45.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-232}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5800000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -6.2e+57)
     t_2
     (if (<= t -4.9e-154)
       t_1
       (if (<= t 1.95e-232)
         x
         (if (<= t 2.8e-141) t_1 (if (<= t 5800000.0) x t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.2e+57) {
		tmp = t_2;
	} else if (t <= -4.9e-154) {
		tmp = t_1;
	} else if (t <= 1.95e-232) {
		tmp = x;
	} else if (t <= 2.8e-141) {
		tmp = t_1;
	} else if (t <= 5800000.0) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-6.2d+57)) then
        tmp = t_2
    else if (t <= (-4.9d-154)) then
        tmp = t_1
    else if (t <= 1.95d-232) then
        tmp = x
    else if (t <= 2.8d-141) then
        tmp = t_1
    else if (t <= 5800000.0d0) then
        tmp = x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -6.2e+57) {
		tmp = t_2;
	} else if (t <= -4.9e-154) {
		tmp = t_1;
	} else if (t <= 1.95e-232) {
		tmp = x;
	} else if (t <= 2.8e-141) {
		tmp = t_1;
	} else if (t <= 5800000.0) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -6.2e+57:
		tmp = t_2
	elif t <= -4.9e-154:
		tmp = t_1
	elif t <= 1.95e-232:
		tmp = x
	elif t <= 2.8e-141:
		tmp = t_1
	elif t <= 5800000.0:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.2e+57)
		tmp = t_2;
	elseif (t <= -4.9e-154)
		tmp = t_1;
	elseif (t <= 1.95e-232)
		tmp = x;
	elseif (t <= 2.8e-141)
		tmp = t_1;
	elseif (t <= 5800000.0)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.2e+57)
		tmp = t_2;
	elseif (t <= -4.9e-154)
		tmp = t_1;
	elseif (t <= 1.95e-232)
		tmp = x;
	elseif (t <= 2.8e-141)
		tmp = t_1;
	elseif (t <= 5800000.0)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+57], t$95$2, If[LessEqual[t, -4.9e-154], t$95$1, If[LessEqual[t, 1.95e-232], x, If[LessEqual[t, 2.8e-141], t$95$1, If[LessEqual[t, 5800000.0], x, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000026e57 or 5.8e6 < t

   1. Initial program 93.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 70.8%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -6.20000000000000026e57 < t < -4.89999999999999997e-154 or 1.9499999999999999e-232 < t < 2.80000000000000012e-141

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 43.8%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]

   if -4.89999999999999997e-154 < t < 1.9499999999999999e-232 or 2.80000000000000012e-141 < t < 5.8e6

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 40.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+167}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;z + \left(x + \left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+84}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(t \cdot \left(b - a\right) - b \cdot \left(2 - y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -4.4e+167)
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (if (<= b -1.02e+15)
       (+ z (+ x (+ (* y (- b z)) (* b (- t 2.0)))))
       (if (<= b 1.7e+84)
         (+ x (+ (* z (- 1.0 y)) t_1))
         (+ a (+ x (- (* t (- b a)) (* b (- 2.0 y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -4.4e+167) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (b <= -1.02e+15) {
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))));
	} else if (b <= 1.7e+84) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = a + (x + ((t * (b - a)) - (b * (2.0 - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-4.4d+167)) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else if (b <= (-1.02d+15)) then
        tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0d0))))
    else if (b <= 1.7d+84) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = a + (x + ((t * (b - a)) - (b * (2.0d0 - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -4.4e+167) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else if (b <= -1.02e+15) {
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))));
	} else if (b <= 1.7e+84) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = a + (x + ((t * (b - a)) - (b * (2.0 - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -4.4e+167:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	elif b <= -1.02e+15:
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))))
	elif b <= 1.7e+84:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = a + (x + ((t * (b - a)) - (b * (2.0 - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -4.4e+167)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	elseif (b <= -1.02e+15)
		tmp = Float64(z + Float64(x + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t - 2.0)))));
	elseif (b <= 1.7e+84)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = Float64(a + Float64(x + Float64(Float64(t * Float64(b - a)) - Float64(b * Float64(2.0 - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -4.4e+167)
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	elseif (b <= -1.02e+15)
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))));
	elseif (b <= 1.7e+84)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = a + (x + ((t * (b - a)) - (b * (2.0 - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+167], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -1.02e+15], N[(z + N[(x + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+84], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.40000000000000007e167

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   if -4.40000000000000007e167 < b < -1.02e15

   1. Initial program 93.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.9%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   4. Taylor expanded in z around inf 84.7%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{-1 \cdot z} \]
   5. Step-by-step derivation

      1. neg-mul-1 84.7%

         \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{\left(-z\right)} \]

   6. Simplified 84.7%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{\left(-z\right)} \]

   if -1.02e15 < b < 1.6999999999999999e84

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 91.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   if 1.6999999999999999e84 < b

   1. Initial program 90.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.1%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in a around inf 92.8%

      \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{-1 \cdot a} \]
   5. Step-by-step derivation

      1. neg-mul-1 92.8%

         \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{\left(-a\right)} \]

   6. Simplified 92.8%

      \[\leadsto \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \color{blue}{\left(-a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+167}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;z + \left(x + \left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+84}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(t \cdot \left(b - a\right) - b \cdot \left(2 - y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;z + \left(x + \left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+86}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (+ (+ x (* b (- (+ y t) 2.0))) t_1)))
   (if (<= b -4.3e+162)
     t_2
     (if (<= b -1.05e+15)
       (+ z (+ x (+ (* y (- b z)) (* b (- t 2.0)))))
       (if (<= b 9e+86) (+ x (+ (* z (- 1.0 y)) t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = (x + (b * ((y + t) - 2.0))) + t_1;
	double tmp;
	if (b <= -4.3e+162) {
		tmp = t_2;
	} else if (b <= -1.05e+15) {
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))));
	} else if (b <= 9e+86) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = (x + (b * ((y + t) - 2.0d0))) + t_1
    if (b <= (-4.3d+162)) then
        tmp = t_2
    else if (b <= (-1.05d+15)) then
        tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0d0))))
    else if (b <= 9d+86) then
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = (x + (b * ((y + t) - 2.0))) + t_1;
	double tmp;
	if (b <= -4.3e+162) {
		tmp = t_2;
	} else if (b <= -1.05e+15) {
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))));
	} else if (b <= 9e+86) {
		tmp = x + ((z * (1.0 - y)) + t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = (x + (b * ((y + t) - 2.0))) + t_1
	tmp = 0
	if b <= -4.3e+162:
		tmp = t_2
	elif b <= -1.05e+15:
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))))
	elif b <= 9e+86:
		tmp = x + ((z * (1.0 - y)) + t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1)
	tmp = 0.0
	if (b <= -4.3e+162)
		tmp = t_2;
	elseif (b <= -1.05e+15)
		tmp = Float64(z + Float64(x + Float64(Float64(y * Float64(b - z)) + Float64(b * Float64(t - 2.0)))));
	elseif (b <= 9e+86)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = (x + (b * ((y + t) - 2.0))) + t_1;
	tmp = 0.0;
	if (b <= -4.3e+162)
		tmp = t_2;
	elseif (b <= -1.05e+15)
		tmp = z + (x + ((y * (b - z)) + (b * (t - 2.0))));
	elseif (b <= 9e+86)
		tmp = x + ((z * (1.0 - y)) + t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -4.3e+162], t$95$2, If[LessEqual[b, -1.05e+15], N[(z + N[(x + N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e+86], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.3000000000000002e162 or 8.99999999999999986e86 < b

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.6%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   if -4.3000000000000002e162 < b < -1.05e15

   1. Initial program 93.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.9%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   4. Taylor expanded in z around inf 84.7%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{-1 \cdot z} \]
   5. Step-by-step derivation

      1. neg-mul-1 84.7%

         \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{\left(-z\right)} \]

   6. Simplified 84.7%

      \[\leadsto \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \color{blue}{\left(-z\right)} \]

   if -1.05e15 < b < 8.99999999999999986e86

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 91.0%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+162}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;z + \left(x + \left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+86}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(\frac{x}{b} - 2\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 200000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (- (/ x b) 2.0)))) (t_2 (* t (- b a))))
   (if (<= t -9.4e+17)
     t_2
     (if (<= t 9.4e-197)
       t_1
       (if (<= t 4.8e-88)
         (* z (- 1.0 y))
         (if (<= t 200000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + ((x / b) - 2.0));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -9.4e+17) {
		tmp = t_2;
	} else if (t <= 9.4e-197) {
		tmp = t_1;
	} else if (t <= 4.8e-88) {
		tmp = z * (1.0 - y);
	} else if (t <= 200000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y + ((x / b) - 2.0d0))
    t_2 = t * (b - a)
    if (t <= (-9.4d+17)) then
        tmp = t_2
    else if (t <= 9.4d-197) then
        tmp = t_1
    else if (t <= 4.8d-88) then
        tmp = z * (1.0d0 - y)
    else if (t <= 200000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + ((x / b) - 2.0));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -9.4e+17) {
		tmp = t_2;
	} else if (t <= 9.4e-197) {
		tmp = t_1;
	} else if (t <= 4.8e-88) {
		tmp = z * (1.0 - y);
	} else if (t <= 200000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y + ((x / b) - 2.0))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -9.4e+17:
		tmp = t_2
	elif t <= 9.4e-197:
		tmp = t_1
	elif t <= 4.8e-88:
		tmp = z * (1.0 - y)
	elif t <= 200000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(Float64(x / b) - 2.0)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -9.4e+17)
		tmp = t_2;
	elseif (t <= 9.4e-197)
		tmp = t_1;
	elseif (t <= 4.8e-88)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 200000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y + ((x / b) - 2.0));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -9.4e+17)
		tmp = t_2;
	elseif (t <= 9.4e-197)
		tmp = t_1;
	elseif (t <= 4.8e-88)
		tmp = z * (1.0 - y);
	elseif (t <= 200000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(N[(x / b), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.4e+17], t$95$2, If[LessEqual[t, 9.4e-197], t$95$1, If[LessEqual[t, 4.8e-88], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 200000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4e17 or 2e11 < t

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.0%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -9.4e17 < t < 9.4000000000000003e-197 or 4.7999999999999999e-88 < t < 2e11

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 79.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 79.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 79.2%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 79.2%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 79.2%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 79.2%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 79.2%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 79.2%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 79.3%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 79.3%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 79.3%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 79.2%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 81.2%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 81.2%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in x around inf 54.2%

      \[\leadsto b \cdot \left(y + \left(\color{blue}{\frac{x}{b}} - 2\right)\right) \]

   if 9.4000000000000003e-197 < t < 4.7999999999999999e-88

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.3 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-202}:\\ \;\;\;\;b \cdot \left(y + \left(\frac{a}{b} - 2\right)\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 380000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -5.3e+15)
     t_1
     (if (<= t 9.5e-202)
       (* b (+ y (- (/ a b) 2.0)))
       (if (<= t 1.28e-86) (* z (- 1.0 y)) (if (<= t 380000.0) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -5.3e+15) {
		tmp = t_1;
	} else if (t <= 9.5e-202) {
		tmp = b * (y + ((a / b) - 2.0));
	} else if (t <= 1.28e-86) {
		tmp = z * (1.0 - y);
	} else if (t <= 380000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-5.3d+15)) then
        tmp = t_1
    else if (t <= 9.5d-202) then
        tmp = b * (y + ((a / b) - 2.0d0))
    else if (t <= 1.28d-86) then
        tmp = z * (1.0d0 - y)
    else if (t <= 380000.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -5.3e+15) {
		tmp = t_1;
	} else if (t <= 9.5e-202) {
		tmp = b * (y + ((a / b) - 2.0));
	} else if (t <= 1.28e-86) {
		tmp = z * (1.0 - y);
	} else if (t <= 380000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -5.3e+15:
		tmp = t_1
	elif t <= 9.5e-202:
		tmp = b * (y + ((a / b) - 2.0))
	elif t <= 1.28e-86:
		tmp = z * (1.0 - y)
	elif t <= 380000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5.3e+15)
		tmp = t_1;
	elseif (t <= 9.5e-202)
		tmp = Float64(b * Float64(y + Float64(Float64(a / b) - 2.0)));
	elseif (t <= 1.28e-86)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 380000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -5.3e+15)
		tmp = t_1;
	elseif (t <= 9.5e-202)
		tmp = b * (y + ((a / b) - 2.0));
	elseif (t <= 1.28e-86)
		tmp = z * (1.0 - y);
	elseif (t <= 380000.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.3e+15], t$95$1, If[LessEqual[t, 9.5e-202], N[(b * N[(y + N[(N[(a / b), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.28e-86], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 380000.0], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.3e15 or 3.8e5 < t

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.0%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -5.3e15 < t < 9.5000000000000001e-202

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 77.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 77.7%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 77.7%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 77.7%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 77.7%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 77.7%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 77.7%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 77.7%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 77.8%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 77.8%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 77.8%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 77.7%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 80.3%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 80.3%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in a around inf 41.7%

      \[\leadsto b \cdot \left(y + \left(\color{blue}{\frac{a}{b}} - 2\right)\right) \]

   if 9.5000000000000001e-202 < t < 1.27999999999999992e-86

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if 1.27999999999999992e-86 < t < 3.8e5

   1. Initial program 99.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 44.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 35.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-23}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.5e-44)
     t_1
     (if (<= a 1.3e-104)
       x
       (if (<= a 1.65e-23) (* t b) (if (<= a 6.8e-5) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e-44) {
		tmp = t_1;
	} else if (a <= 1.3e-104) {
		tmp = x;
	} else if (a <= 1.65e-23) {
		tmp = t * b;
	} else if (a <= 6.8e-5) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-4.5d-44)) then
        tmp = t_1
    else if (a <= 1.3d-104) then
        tmp = x
    else if (a <= 1.65d-23) then
        tmp = t * b
    else if (a <= 6.8d-5) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e-44) {
		tmp = t_1;
	} else if (a <= 1.3e-104) {
		tmp = x;
	} else if (a <= 1.65e-23) {
		tmp = t * b;
	} else if (a <= 6.8e-5) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.5e-44:
		tmp = t_1
	elif a <= 1.3e-104:
		tmp = x
	elif a <= 1.65e-23:
		tmp = t * b
	elif a <= 6.8e-5:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.5e-44)
		tmp = t_1;
	elseif (a <= 1.3e-104)
		tmp = x;
	elseif (a <= 1.65e-23)
		tmp = Float64(t * b);
	elseif (a <= 6.8e-5)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.5e-44)
		tmp = t_1;
	elseif (a <= 1.3e-104)
		tmp = x;
	elseif (a <= 1.65e-23)
		tmp = t * b;
	elseif (a <= 6.8e-5)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e-44], t$95$1, If[LessEqual[a, 1.3e-104], x, If[LessEqual[a, 1.65e-23], N[(t * b), $MachinePrecision], If[LessEqual[a, 6.8e-5], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4999999999999999e-44 or 6.7999999999999999e-5 < a

   1. Initial program 92.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 51.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -4.4999999999999999e-44 < a < 1.30000000000000001e-104 or 1.6500000000000001e-23 < a < 6.7999999999999999e-5

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 32.7%

      \[\leadsto \color{blue}{x} \]

   if 1.30000000000000001e-104 < a < 1.6500000000000001e-23

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 87.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around inf 42.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(1 - \frac{a}{b}\right)\right)} \]

   5. Taylor expanded in a around 0 42.4%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-23}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+58} \lor \neg \left(b \leq 3.4 \cdot 10^{+85}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -1.3e+58) (not (<= b 3.4e+85)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ (* z (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -1.3e+58) || !(b <= 3.4e+85)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((z * (1.0 - y)) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-1.3d+58)) .or. (.not. (b <= 3.4d+85))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + ((z * (1.0d0 - y)) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -1.3e+58) || !(b <= 3.4e+85)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((z * (1.0 - y)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -1.3e+58) or not (b <= 3.4e+85):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + ((z * (1.0 - y)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -1.3e+58) || !(b <= 3.4e+85))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -1.3e+58) || ~((b <= 3.4e+85)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + ((z * (1.0 - y)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.3e+58], N[Not[LessEqual[b, 3.4e+85]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.29999999999999994e58 or 3.4000000000000003e85 < b

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   if -1.29999999999999994e58 < b < 3.4000000000000003e85

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 89.7%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+58} \lor \neg \left(b \leq 3.4 \cdot 10^{+85}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-49}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -4.5e+50)
     t_1
     (if (<= b -3.4e-49)
       (+ (+ x a) (* z (- 1.0 y)))
       (if (<= b 2.8e+117) (+ x (+ z (* a (- 1.0 t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.5e+50) {
		tmp = t_1;
	} else if (b <= -3.4e-49) {
		tmp = (x + a) + (z * (1.0 - y));
	} else if (b <= 2.8e+117) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-4.5d+50)) then
        tmp = t_1
    else if (b <= (-3.4d-49)) then
        tmp = (x + a) + (z * (1.0d0 - y))
    else if (b <= 2.8d+117) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.5e+50) {
		tmp = t_1;
	} else if (b <= -3.4e-49) {
		tmp = (x + a) + (z * (1.0 - y));
	} else if (b <= 2.8e+117) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4.5e+50:
		tmp = t_1
	elif b <= -3.4e-49:
		tmp = (x + a) + (z * (1.0 - y))
	elif b <= 2.8e+117:
		tmp = x + (z + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4.5e+50)
		tmp = t_1;
	elseif (b <= -3.4e-49)
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	elseif (b <= 2.8e+117)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4.5e+50)
		tmp = t_1;
	elseif (b <= -3.4e-49)
		tmp = (x + a) + (z * (1.0 - y));
	elseif (b <= 2.8e+117)
		tmp = x + (z + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+50], t$95$1, If[LessEqual[b, -3.4e-49], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+117], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.50000000000000014e50 or 2.79999999999999997e117 < b

   1. Initial program 91.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 74.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -4.50000000000000014e50 < b < -3.40000000000000005e-49

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 95.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 69.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 69.0%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 69.0%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 69.0%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 69.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 69.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 69.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 68.8%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 68.8%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 68.8%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 69.0%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 68.8%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 68.8%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in b around 0 69.1%

      \[\leadsto \color{blue}{\left(a + x\right) - z \cdot \left(y - 1\right)} \]

   if -3.40000000000000005e-49 < b < 2.79999999999999997e117

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.5%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   4. Taylor expanded in y around inf 92.9%

      \[\leadsto \left(x + \color{blue}{y \cdot \left(\left(b + \frac{b \cdot \left(t - 2\right)}{y}\right) - z\right)}\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

   5. Taylor expanded in x around inf 75.7%

      \[\leadsto \color{blue}{x} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-49}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;t\_1 - t \cdot a\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+117}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -4.7e+58)
     (- t_1 (* t a))
     (if (<= b 3.7e+117) (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.7e+58) {
		tmp = t_1 - (t * a);
	} else if (b <= 3.7e+117) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-4.7d+58)) then
        tmp = t_1 - (t * a)
    else if (b <= 3.7d+117) then
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -4.7e+58) {
		tmp = t_1 - (t * a);
	} else if (b <= 3.7e+117) {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -4.7e+58:
		tmp = t_1 - (t * a)
	elif b <= 3.7e+117:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -4.7e+58)
		tmp = Float64(t_1 - Float64(t * a));
	elseif (b <= 3.7e+117)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -4.7e+58)
		tmp = t_1 - (t * a);
	elseif (b <= 3.7e+117)
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+58], N[(t$95$1 - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+117], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.69999999999999972e58

   1. Initial program 93.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 72.1%

         \[\leadsto \color{blue}{\left(-a \cdot t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. distribute-rgt-neg-in 72.1%

         \[\leadsto \color{blue}{a \cdot \left(-t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{a \cdot \left(-t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -4.69999999999999972e58 < b < 3.6999999999999999e117

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 89.2%

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   if 3.6999999999999999e117 < b

   1. Initial program 88.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 86.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+117}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-11}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.8e+60)
   (* t (- b a))
   (if (<= t 7.2e-11)
     (+ (+ x a) (* z (- 1.0 y)))
     (- (* b (- (+ y t) 2.0)) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+60) {
		tmp = t * (b - a);
	} else if (t <= 7.2e-11) {
		tmp = (x + a) + (z * (1.0 - y));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.8d+60)) then
        tmp = t * (b - a)
    else if (t <= 7.2d-11) then
        tmp = (x + a) + (z * (1.0d0 - y))
    else
        tmp = (b * ((y + t) - 2.0d0)) - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.8e+60) {
		tmp = t * (b - a);
	} else if (t <= 7.2e-11) {
		tmp = (x + a) + (z * (1.0 - y));
	} else {
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.8e+60:
		tmp = t * (b - a)
	elif t <= 7.2e-11:
		tmp = (x + a) + (z * (1.0 - y))
	else:
		tmp = (b * ((y + t) - 2.0)) - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.8e+60)
		tmp = Float64(t * Float64(b - a));
	elseif (t <= 7.2e-11)
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.8e+60)
		tmp = t * (b - a);
	elseif (t <= 7.2e-11)
		tmp = (x + a) + (z * (1.0 - y));
	else
		tmp = (b * ((y + t) - 2.0)) - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.8e+60], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-11], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.79999999999999999e60

   1. Initial program 90.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 69.9%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -5.79999999999999999e60 < t < 7.19999999999999969e-11

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 75.8%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 75.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 75.0%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 75.0%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 75.0%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 75.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 75.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 75.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 74.9%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 74.9%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 74.9%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 75.0%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 76.6%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 76.6%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in b around 0 74.9%

      \[\leadsto \color{blue}{\left(a + x\right) - z \cdot \left(y - 1\right)} \]

   if 7.19999999999999969e-11 < t

   1. Initial program 95.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 80.5%

         \[\leadsto \color{blue}{\left(-a \cdot t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. distribute-rgt-neg-in 80.5%

         \[\leadsto \color{blue}{a \cdot \left(-t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 80.5%

      \[\leadsto \color{blue}{a \cdot \left(-t\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-11}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+59} \lor \neg \left(t \leq 5.5 \cdot 10^{+15}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.6e+59) (not (<= t 5.5e+15)))
   (* t (- b a))
   (+ (+ x a) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.6e+59) || !(t <= 5.5e+15)) {
		tmp = t * (b - a);
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.6d+59)) .or. (.not. (t <= 5.5d+15))) then
        tmp = t * (b - a)
    else
        tmp = (x + a) + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.6e+59) || !(t <= 5.5e+15)) {
		tmp = t * (b - a);
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.6e+59) or not (t <= 5.5e+15):
		tmp = t * (b - a)
	else:
		tmp = (x + a) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.6e+59) || !(t <= 5.5e+15))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.6e+59) || ~((t <= 5.5e+15)))
		tmp = t * (b - a);
	else
		tmp = (x + a) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.6e+59], N[Not[LessEqual[t, 5.5e+15]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5999999999999999e59 or 5.5e15 < t

   1. Initial program 93.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 71.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -3.5999999999999999e59 < t < 5.5e15

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 75.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 74.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 74.2%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 74.2%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 74.2%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 74.2%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 74.2%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 74.2%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 74.1%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 74.1%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 74.1%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 74.2%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 75.7%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 75.7%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in b around 0 73.5%

      \[\leadsto \color{blue}{\left(a + x\right) - z \cdot \left(y - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+59} \lor \neg \left(t \leq 5.5 \cdot 10^{+15}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- t))))
   (if (<= t -1.45e+39)
     t_1
     (if (<= t 2600000000000.0) x (if (<= t 2.05e+214) t_1 (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (t <= -1.45e+39) {
		tmp = t_1;
	} else if (t <= 2600000000000.0) {
		tmp = x;
	} else if (t <= 2.05e+214) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * -t
    if (t <= (-1.45d+39)) then
        tmp = t_1
    else if (t <= 2600000000000.0d0) then
        tmp = x
    else if (t <= 2.05d+214) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (t <= -1.45e+39) {
		tmp = t_1;
	} else if (t <= 2600000000000.0) {
		tmp = x;
	} else if (t <= 2.05e+214) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * -t
	tmp = 0
	if t <= -1.45e+39:
		tmp = t_1
	elif t <= 2600000000000.0:
		tmp = x
	elif t <= 2.05e+214:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(-t))
	tmp = 0.0
	if (t <= -1.45e+39)
		tmp = t_1;
	elseif (t <= 2600000000000.0)
		tmp = x;
	elseif (t <= 2.05e+214)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * -t;
	tmp = 0.0;
	if (t <= -1.45e+39)
		tmp = t_1;
	elseif (t <= 2600000000000.0)
		tmp = x;
	elseif (t <= 2.05e+214)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * (-t)), $MachinePrecision]}, If[LessEqual[t, -1.45e+39], t$95$1, If[LessEqual[t, 2600000000000.0], x, If[LessEqual[t, 2.05e+214], t$95$1, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45000000000000015e39 or 2.6e12 < t < 2.05e214

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 78.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(1 - \frac{a}{b}\right)\right)} \]

   5. Taylor expanded in b around 0 41.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.6%

         \[\leadsto \color{blue}{-a \cdot t} \]

      2. *-commutative 41.6%

         \[\leadsto -\color{blue}{t \cdot a} \]

      3. distribute-rgt-neg-in 41.6%

         \[\leadsto \color{blue}{t \cdot \left(-a\right)} \]

   7. Simplified 41.6%

      \[\leadsto \color{blue}{t \cdot \left(-a\right)} \]

   if -1.45000000000000015e39 < t < 2.6e12

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 32.3%

      \[\leadsto \color{blue}{x} \]

   if 2.05e214 < t

   1. Initial program 96.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 78.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around inf 78.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(1 - \frac{a}{b}\right)\right)} \]

   5. Taylor expanded in a around 0 62.3%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 2600000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+214}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+32} \lor \neg \left(t \leq 530000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.05e+32) (not (<= t 530000000000.0))) (* t (- b a)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.05e+32) || !(t <= 530000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.05d+32)) .or. (.not. (t <= 530000000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.05e+32) || !(t <= 530000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.05e+32) or not (t <= 530000000000.0):
		tmp = t * (b - a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.05e+32) || !(t <= 530000000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.05e+32) || ~((t <= 530000000000.0)))
		tmp = t * (b - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.05e+32], N[Not[LessEqual[t, 530000000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.0499999999999999e32 or 5.3e11 < t

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 69.3%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -2.0499999999999999e32 < t < 5.3e11

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 32.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+32} \lor \neg \left(t \leq 530000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+65} \lor \neg \left(t \leq 2.6 \cdot 10^{+21}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.8e+65) (not (<= t 2.6e+21))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.8e+65) || !(t <= 2.6e+21)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-7.8d+65)) .or. (.not. (t <= 2.6d+21))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.8e+65) || !(t <= 2.6e+21)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.8e+65) or not (t <= 2.6e+21):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.8e+65) || !(t <= 2.6e+21))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.8e+65) || ~((t <= 2.6e+21)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.8e+65], N[Not[LessEqual[t, 2.6e+21]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -7.7999999999999996e65 or 2.6e21 < t

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 76.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around inf 67.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot \left(1 - \frac{a}{b}\right)\right)} \]

   5. Taylor expanded in a around 0 36.9%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -7.7999999999999996e65 < t < 2.6e21

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 31.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+65} \lor \neg \left(t \leq 2.6 \cdot 10^{+21}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e-42) x (if (<= x 4.8e-30) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e-42) {
		tmp = x;
	} else if (x <= 4.8e-30) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.5d-42)) then
        tmp = x
    else if (x <= 4.8d-30) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e-42) {
		tmp = x;
	} else if (x <= 4.8e-30) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e-42:
		tmp = x
	elif x <= 4.8e-30:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e-42)
		tmp = x;
	elseif (x <= 4.8e-30)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e-42)
		tmp = x;
	elseif (x <= 4.8e-30)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e-42], x, If[LessEqual[x, 4.8e-30], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999948e-42 or 4.7999999999999997e-30 < x

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 33.1%

      \[\leadsto \color{blue}{x} \]

   if -9.49999999999999948e-42 < x < 4.7999999999999997e-30

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 79.3%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

   4. Taylor expanded in t around 0 49.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate--l+ 49.0%

         \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

      2. +-commutative 49.0%

         \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

      3. associate--r+ 49.0%

         \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

      4. +-commutative 49.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

      5. sub-neg 49.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      6. metadata-eval 49.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      7. associate-*r/ 49.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

      8. mul-1-neg 49.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

      9. unsub-neg 49.0%

         \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

      10. associate-*r/ 49.0%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

      11. associate-*l/ 50.9%

          \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. Simplified 50.9%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

   7. Taylor expanded in a around inf 14.5%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 11.1% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 95.7%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in b around inf 77.0%

   \[\leadsto \color{blue}{b \cdot \left(\left(t + \left(y + \frac{x}{b}\right)\right) - \left(2 + \left(\frac{a \cdot \left(t - 1\right)}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]

4. Taylor expanded in t around 0 52.1%

   \[\leadsto \color{blue}{b \cdot \left(\left(y + \frac{x}{b}\right) - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)} \]
5. Step-by-step derivation

   1. associate--l+ 52.1%

      \[\leadsto b \cdot \color{blue}{\left(y + \left(\frac{x}{b} - \left(2 + \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right)\right)\right)} \]

   2. +-commutative 52.1%

      \[\leadsto b \cdot \left(y + \left(\frac{x}{b} - \color{blue}{\left(\left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right) + 2\right)}\right)\right) \]

   3. associate--r+ 52.1%

      \[\leadsto b \cdot \left(y + \color{blue}{\left(\left(\frac{x}{b} - \left(-1 \cdot \frac{a}{b} + \frac{z \cdot \left(y - 1\right)}{b}\right)\right) - 2\right)}\right) \]

   4. +-commutative 52.1%

      \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(\frac{z \cdot \left(y - 1\right)}{b} + -1 \cdot \frac{a}{b}\right)}\right) - 2\right)\right) \]

   5. sub-neg 52.1%

      \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \color{blue}{\left(y + \left(-1\right)\right)}}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

   6. metadata-eval 52.1%

      \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z \cdot \left(y + \color{blue}{-1}\right)}{b} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

   7. associate-*r/ 52.1%

      \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{z \cdot \frac{y + -1}{b}} + -1 \cdot \frac{a}{b}\right)\right) - 2\right)\right) \]

   8. mul-1-neg 52.1%

      \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(z \cdot \frac{y + -1}{b} + \color{blue}{\left(-\frac{a}{b}\right)}\right)\right) - 2\right)\right) \]

   9. unsub-neg 52.1%

      \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \color{blue}{\left(z \cdot \frac{y + -1}{b} - \frac{a}{b}\right)}\right) - 2\right)\right) \]

   10. associate-*r/ 52.1%

       \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z \cdot \left(y + -1\right)}{b}} - \frac{a}{b}\right)\right) - 2\right)\right) \]

   11. associate-*l/ 52.9%

       \[\leadsto b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\color{blue}{\frac{z}{b} \cdot \left(y + -1\right)} - \frac{a}{b}\right)\right) - 2\right)\right) \]

6. Simplified 52.9%

   \[\leadsto \color{blue}{b \cdot \left(y + \left(\left(\frac{x}{b} - \left(\frac{z}{b} \cdot \left(y + -1\right) - \frac{a}{b}\right)\right) - 2\right)\right)} \]

7. Taylor expanded in a around inf 9.5%

   \[\leadsto \color{blue}{a} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))